The important detail concerning the accident that kills Myrtle in The Great Gatsby is that Myrtle is hailing the car, because she thinks Tom, the person she is having the affair with, is driving the car.
Earlier in the day when Tom stops for gas at the Wilson's business he is driving Gatsby's car. From the room in which she is locked, Myrtle sees Tom and the car.
When she sees the car coming her way that night, she runs out to flag it down, assuming Tom is inside. That's how she gets hit.
Of course, Daisy--Tom's wife, which is convenient--is driving and Gatsby is the passenger. Tom is not in the car.
Apparently, Myrtle assumes Tom is driving the car and that he will stop for her. She is trying to escape "captivity" at the hands of her husband, Wilson. Daisy, though, an inexperienced driver, runs her over instead, presumably by mistake.
A series of events lead up to Myrtle's death on the night in question. First, Tom stops at the station in Gatsby's car. Then, Myrtle and Wilson fight. He locks her up because he fears that she is going to try to leave him. She is becoming desperate for she fears that she is losing Tom as well. Meanwhile, tensions between Gatsby and Tom as well as Daisy's own sense of being trapped in the middle lead to an afternoon of drinking that relaxes judgement. Gatsby allows Daisy to drive his car, knowing that she is upset and intoxicated. This is the event that leads the car to be coming down the road at the exact moment Myrtle makes her escape. She sees the car and knows that Tom should be the one driving, so she ruins into the road to stop him. She is trying to escape but Daisy is running from her own demons and does not see her in time to avoid her. Knowing what she has done, she does not stop. She keeps on running.
There is a distinct causal chain to the outcome of this evening. One thing leads to another and a tragedy is set in motion. Had Gatsby not offered Tom his car, the outcome would have been different for all concerned. While the offer of the car seems insignificant, it is the catalyst for the way things turn out in the end.
On the night that she died, Myrtle Wilson had been locked up in a room by her husband. He had found out that she was having an affair (he did not know with whom) and he was going to keep her locked up until they could move somewhere else.
That night, she managed to get out of the locked room. Then she ran out into the road and was run over by Daisy Buchanan. The car belongs to Gatsby, but it is Daisy who is driving it.
You can find further details in Chapter 7 if you need them.